Wave fields and transport in plasma
Analysis of different kinds of wave fields in plasma induced by waves propagating in plasma is made. It is shown that the possible cause of collisionless diffusion is scattering of particles on complex field arising as a result of summarising of many wave modes. Виповнено аналіз різних типів хвильов...
Збережено в:
| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2003 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2003
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/110488 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Wave fields and transport in plasma / V.I. Khvesyuk // Вопросы атомной науки и техники. — 2003. — № 1. — С. 68-69. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859658082951364608 |
|---|---|
| author | Khvesyuk, V.I. |
| author_facet | Khvesyuk, V.I. |
| citation_txt | Wave fields and transport in plasma / V.I. Khvesyuk // Вопросы атомной науки и техники. — 2003. — № 1. — С. 68-69. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Analysis of different kinds of wave fields in plasma induced by waves propagating in plasma is made. It is shown that the possible cause of collisionless diffusion is scattering of particles on complex field arising as a result of summarising of many wave modes.
Виповнено аналіз різних типів хвильових полів, які викликані розповсюдженням хвиль у плазмі. Показано, що причиною беззіштовхувальної дифузії може бути розсіювання частинок у складних полях, які виникають внаслідок складання багатьох хвильових мод.
Выполнен анализ различных типов волновых полей, вызываемых распространяющимися в плазме волнами. Показано, что причиной бесстолкновительной диффузии может являться рассеяние частиц на сложных полях, возникающих в результате сложения многих волновых мод.
|
| first_indexed | 2025-12-07T13:41:04Z |
| format | Article |
| fulltext |
WAVE FIELDS AND TRANSPORT IN PLASMA
V.I. Khvesyuk
Bauman Moscow State Technical University,
2nd Baumanskaya Str., 5, 105005 Moscow, Russia, e-mail: khves@power.bmstu.ru
Analysis of different kinds of wave fields in plasma induced by waves propagating in plasma is made. It is shown that
the possible cause of collisionless diffusion is scattering of particles on complex field arising as a result of summarising
of many wave modes.
PACS: 52.25.Fi; 52.25.Gj; 52.35.Ra; 52.35.Kt
1. INTRODUCTION
As a rule models of collisionless anomalous transport
in plasma are based on quasi-linear theory [1-4]. The
simplest approach of anomalous processes takes into
account interactions only between two subjects in plasma:
charged particles (electron and ions) and low amplitude
wave modes. Interactions “wave-wave” and “particle-
particle” are not taken into account.
Recently a new model of the wave fields in tokamaks
have suggested by W. Horton et al. [5, 6]. This model
focuses attention on formation of large electrostatic wave
fluctuation (wave packets) representing the summation of
many wave modes propagating in plasma.
In this paper similar approach for cylindrical plasma is
discussed. Really model implies following picture of the
wave field. It includes two components. First component
is the background of the weak wave oscillations in
plasma. Their averaged a such that they exert negligible
action on particles. On the background of the weak
oscillations large wave packets are formed. It is the
second feature of the model. In the frame of this approach
the reason of anomalous transport is the influence of the
large field fluctuations (wave packets) on particles.
For cylindrical plasma at fixed radius r the set of
azimuthal wave modes appears. These modes satisfy the
conditions of existence: 2πr/λ=integer number (λ is the
wavelength), and they have similar amplitude values.
Different modes rotate with different velocities. On the
background of these modes the wave packets arise and
decay. At different radii of non-uniform plasma different
sets of wave modes are formed. In the whole the complex
picture of the wave field arises.
2. TRANSPORT IN CYLINDRICAL
MAGNETIZED PLASMA
It is supposed that amplitudes of all wave modes at
fixed radius r are the same end they are equal E0. Here
wave modes with the same phase velocity are considered.
In this case total electrostatic field takes the form
E s t E k s t n
s
v t
phn N
n N
( , ) cos( ) sin= − −
= −
=
∑0 0 0ω ω∆ , (1)
where s is the azimuthal coordinate, vph=vph(r) is the phase
velocity, E0= E0(r), k0 and ω0 are the wave vector and
frequency, ∆ω is the frequency shift. All parameters of
the plasma, magnetic field and electric field (1) are
choose in such a way that the drift approach to the particle
motion is fulfilled. Then corresponding equation is
dr
dt
E s r t
B r
= ( , , )
( ) , (2)
where B(r) is the magnetic field.
The phase angle of the wave θ is introduced. Than the
map of Eq. (2) with electric field Eq. (1) in (r, θ) phase
plane is the following:
r r K rj j j+ = +1 ( ) cosθ ,
(3)
θ θ
ω
ωj j+ = +1
02 ∆
.
Note that K
E r
B r
T= < >0 ( )
( )
, where <T> is averaged
time of the wave packets passage with the respect of
magnetized particles. Condition of stochastization is [7]
K
r
r
K
r
j
j j
= − = >
+δ
δ
δ
δ
1
1 1~ .
Therefore K has to be a function of the radius in order to
satisfy the stochastization condition
Some results of calculations are presented in the
Figure.
3. CONDITION OF AMBIPOLAR
TRANSPORT
In this Section the ambipolar condition in the context
of considered approach is formulated. In the simplest case
of fulfilling of drift approach for electrons and ions within
any wave packets this task is considered. Equality of
electrons and ions transport flows from equality of
averaged direct velocities of different particles with
respect to averaged group velocity of wave packets. In the
case ∇ ≠B 0 the following expression is obtained:
< > − < > ± = < > + < >V v
E
B V v
E
ZBe g
r
i g
r , (4)
where Er is the stationary radial electric field, B=Bz(r) is
confining magnetic field directed along z-axis, Z is the
ion charge number, <Ve> and <Vi> are averaged gradient
drift velocities of electrons and ions, respectively, <vg> is
the averaged wave group velocity. Signs “+” or “–” are
determined by the direction of Er.
68 Problems of Atomic Science and Technology. 2003. № 1. Series: Plasma Physics (9). P. 68-69
Example of calculation of the map (Eq. (3))
4. SUPPRESSION OF ANOMALOUS
TRANSPORT
In Ref. [8] it was shown that the considered model
explains in principle the reason of suppression of
anomalous transport. In mentioned work only influence of
steady state electric field Er was taken into account.
Here the possible reason of increase of Er due to the
growth of temperature is discussed. It is well known that
namely added heating results in rise of Er and suppression
of the transport in tokamaks [9]. Gradient drift velocities
are
< > =V
k T
eBe
B e
Bχ ,
< > =V
k T
ZeBi
B i
Bχ ,
where kB is the Boltzmann constant, Te and Ti are electron
and ion temperatures, respectively, χ B B B= ∇ / .
Averaged time of interaction of the particle (electron)
with the wave packet is (see Eq.(1)):
< > =
− < >
τ h
V v
E
Be g
r
, (5)
where h is the averaged width of wave packet. Averaged
displacement of particles as a result of the interaction is
< > =
< >
< >∆ r
E
B
~
τ , (6)
where < >~E is averaged electric field of the wave
packet.
We assume that <vg> is independent on temperature.
Then from Eqs. (5) and (6) follows that increasing Te and
Ti lead to decreasing < >τ and < >∆ r . The initial
reason is increase of averaged gradient drift velocities
under increase of plasma temperature. Eq. (4) establishes
the dependence of Er on plasma temperature:
E V V v Br i e g= < > − < > + < >2 .
Here Er is increasing dependence on plasma temperature.
Therefore increase of the temperature leads to increase
of Er. In turn < >τ and < >∆ r are decrease in
agreement with Eqs. (5) and (6). The similar dependence
is observed in experimental investigations [9].
ACKNOWLEDGMENTS
This work was supported in part by the International
Science and Technology Center, project no. 1260.
REFERENCES
1. A.A. Vedenov, E.P. Velikhov, and R.Z. Sagdeev //
Nucl. Fusion, 1961, v. 1, P. 82.
2. W.E. Drummond and D.Pines // Nucl. Fusion Suppl.,
1962, v. 3, P. 1049.
3. B.B. Kadomtsev, Plasma turbulence. Academic
Press, New York, 1965.
4. R.C. Davidson and N.A. Krall // Nucl. Fusion, 11977,
v. 17, P. 1313.
5. W. Horton, H.-B. Park, J.-M. Kwon, et al. // Phys.
plasmas, 1998, v. 5. P. 3910.
6. J.-M. Kwon, W. Horton, P. Zhu, et al. // Phys.
plasmas, 2000, v. 7. P. 1168.
7. G.M. Zaslavsky, R.Z. Sagdeev, Introduction in non-
linear physics. Nauka, Moscow, 1988.
8. V.I. Khvesyuk, A.Yu. Chirkov, and A.V. Kovalev //
Plasma Phys. Reports., 2002, v. 28, No. 9, P. 787.
9. K.H. Burrel // Phys. Plasmas, 1997, v. 4, P. 1499.
ХВИЛЬОВІ ПОЛЯ Й ТРАНСПОРТ У ПЛАЗМІ
В.І. Хвесюк
Виповнено аналіз різних типів хвильових полів, які викликані розповсюдженням хвиль у плазмі. Показано, що
причиною беззіштовхувальної дифузії може бути розсіювання частинок у складних полях, які виникають
внаслідок складання багатьох хвильових мод.
ВОЛНОВЫЕ ПОЛЯ И ТРАНСПОРТ В ПЛАЗМЕ
В.И. Хвесюк
Выполнен анализ различных типов волновых полей, вызываемых распространяющимися в плазме волнами.
Показано, что причиной бесстолкновительной диффузии может являться рассеяние частиц на сложных полях,
возникающих в результате сложения многих волновых мод.
69
2nd Baumanskaya Str., 5, 105005 Moscow, Russia, e-mail: khves@power.bmstu.ru
хвильові поля й транспорт у плазмі
ВОЛНОВЫЕ ПОЛЯ И ТРАНСПОРТ В ПЛАЗМЕ
|
| id | nasplib_isofts_kiev_ua-123456789-110488 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:41:04Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Khvesyuk, V.I. 2017-01-04T14:21:34Z 2017-01-04T14:21:34Z 2003 Wave fields and transport in plasma / V.I. Khvesyuk // Вопросы атомной науки и техники. — 2003. — № 1. — С. 68-69. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.25.Fi; 52.25.Gj; 52.35.Ra; 52.35.Kt https://nasplib.isofts.kiev.ua/handle/123456789/110488 Analysis of different kinds of wave fields in plasma induced by waves propagating in plasma is made. It is shown that the possible cause of collisionless diffusion is scattering of particles on complex field arising as a result of summarising of many wave modes. Виповнено аналіз різних типів хвильових полів, які викликані розповсюдженням хвиль у плазмі. Показано, що причиною беззіштовхувальної дифузії може бути розсіювання частинок у складних полях, які виникають внаслідок складання багатьох хвильових мод. Выполнен анализ различных типов волновых полей, вызываемых распространяющимися в плазме волнами. Показано, что причиной бесстолкновительной диффузии может являться рассеяние частиц на сложных полях, возникающих в результате сложения многих волновых мод. This work was supported in part by the International Science and Technology Center, project no. 1260 en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Basic plasma physics Wave fields and transport in plasma Хвильові поля й транспорт у плазмі Волновые поля и транспорт в плазме Article published earlier |
| spellingShingle | Wave fields and transport in plasma Khvesyuk, V.I. Basic plasma physics |
| title | Wave fields and transport in plasma |
| title_alt | Хвильові поля й транспорт у плазмі Волновые поля и транспорт в плазме |
| title_full | Wave fields and transport in plasma |
| title_fullStr | Wave fields and transport in plasma |
| title_full_unstemmed | Wave fields and transport in plasma |
| title_short | Wave fields and transport in plasma |
| title_sort | wave fields and transport in plasma |
| topic | Basic plasma physics |
| topic_facet | Basic plasma physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110488 |
| work_keys_str_mv | AT khvesyukvi wavefieldsandtransportinplasma AT khvesyukvi hvilʹovípolâitransportuplazmí AT khvesyukvi volnovyepolâitransportvplazme |